Its probably true of most animals. I raised a couple of pigs and we intentionally never fed them any meat, even though they'd probably eat it, because we didnt want them to get a taste for it
I suspect it is not just when fruit is scarce many if not most primates are omnivores. Fruit is likely easier than meat most of the time but meat contains dense nutrients. Macaques e.g crab eating macaques routinely eat meat.
Is that not the case in Central/South America?
https://www.ucdavis.edu/climate/news/carnivorous-feeding-squ...